SOLUTIONS TO THE EXTENDED GRAETZ PROBLEM FOR A POWER-MODEL FLUID WITH VISCOUS DISSIPATION AND DIFFERENT ENTRANCE BOUNDARY CONDITIONS

Abstract

The transport phenomena of the extended Graetz problem with three different entrance boundary conditions are discussed. The expansion coefficients of the solution corresponding to the different conditions play an important role in effecting the solution form. The solution, assuming that the entrance boundary conditions for both temperature and energy flux (TFBC) are continuous, is the same as that for the problem in which the downstream region was considered infinite. Among all the procedures used, the computational procedures for TFBC are the simplest. The TFBC condition is recommended for use in analyzing the problem. Results show that temperature profiles and local Nussell number are influenced by Piclet number and different entrance boundary conditions. In addition, it is also shown that the asymptotic Nussell numbers for the three different conditions are the same.